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題名 探討半純函數指定兩個值之相關問題
On meromorphic functions with two prescribed values作者 張靜華
Chang, Ching Hua貢獻者 陳天進
Chen, Ten Ging
張靜華
Chang, Ching Hua關鍵詞 半純函數
Prescribed Values日期 2009 上傳時間 9-May-2016 15:25:42 (UTC+8) 摘要 在這篇論文裡，我們探討半純函數指定兩個值之相關問題。特別地，我們探討純函數指定0-1集，同時，我們論證了有關離散型複數數列之一些有趣的結果，利用它們得到關於指定0-1集純函數存在性的必要條件。
In this thesis, we study meromorphic functions with two prescribed values. Especially, entire functions with prescribed zero-one sets. Also, we develop the growth criterion for discrete complex sequences and obtain some interesting results. Using the order of discrete sequences, we obtain a necessary condition for the existence of entire functions with prescribed zero-one set.
謝辭 i Abstract ii 中文摘要 iii Introduction 1 Meromorphic Functions with Prescribed Zero-Pole Sets 2 The Growth of Discrete Sequences 6 Basic Theory of Value Distribution 18 Entire Functions with Prescribed Zero-One Sets 25 References 34參考文獻 [1] L. V. Ahlfors, Complex analysis, Third edition,McGraw-Hill, 1979. [2] J. B. Conway, Functions of one complex variable, Second edition, Springer-Verlag, 1973. [3] F. Gross, Factorization of meromorphic functions, U. S. Government Printing Office, Washington, D. C. , 1972. [4] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. [5] R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Gauthiers-Villars, Paris, 1929. [6] M. Ozawa, On the zero-one set of an entire function, Kodai Math. J. , 2 (1979), 194--199. [7] L. A. Rubel and C. C. Yang, Interpolation and unavoidable families of meromorphic functions, Mich. Math. J. , 20 (1973), 289--296. [8] L. Yang, Value distribution theory, Berlin Heidelberg: Springer-Verlag, Beijing:Science Press, 1993. [9] C. C. Yang and C. T. Chuang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988. [10] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, 2003. [11] H. X. Yi, Some theorems on systems of meromorphic functions, J. Shandong Univ. , 32 (1997), No.3, 241--247. 描述 碩士
國立政治大學
應用數學系
96972001資料來源 http://thesis.lib.nccu.edu.tw/record/#G0096972001 資料類型 thesis dc.contributor.advisor 陳天進 zh_TW dc.contributor.advisor Chen, Ten Ging en_US dc.contributor.author (Authors) 張靜華 zh_TW dc.contributor.author (Authors) Chang, Ching Hua en_US dc.creator (作者) 張靜華 zh_TW dc.creator (作者) Chang, Ching Hua en_US dc.date (日期) 2009 en_US dc.date.accessioned 9-May-2016 15:25:42 (UTC+8) - dc.date.available 9-May-2016 15:25:42 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 15:25:42 (UTC+8) - dc.identifier (Other Identifiers) G0096972001 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95256 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 96972001 zh_TW dc.description.abstract (摘要) 在這篇論文裡，我們探討半純函數指定兩個值之相關問題。特別地，我們探討純函數指定0-1集，同時，我們論證了有關離散型複數數列之一些有趣的結果，利用它們得到關於指定0-1集純函數存在性的必要條件。 zh_TW dc.description.abstract (摘要) In this thesis, we study meromorphic functions with two prescribed values. Especially, entire functions with prescribed zero-one sets. Also, we develop the growth criterion for discrete complex sequences and obtain some interesting results. Using the order of discrete sequences, we obtain a necessary condition for the existence of entire functions with prescribed zero-one set. en_US dc.description.abstract (摘要) 謝辭 i Abstract ii 中文摘要 iii Introduction 1 Meromorphic Functions with Prescribed Zero-Pole Sets 2 The Growth of Discrete Sequences 6 Basic Theory of Value Distribution 18 Entire Functions with Prescribed Zero-One Sets 25 References 34 - dc.description.tableofcontents 謝辭 i Abstract ii 中文摘要 iii Introduction 1 Meromorphic Functions with Prescribed Zero-Pole Sets 2 The Growth of Discrete Sequences 6 Basic Theory of Value Distribution 18 Entire Functions with Prescribed Zero-One Sets 25 References 34 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0096972001 en_US dc.subject (關鍵詞) 半純函數 zh_TW dc.subject (關鍵詞) Prescribed Values en_US dc.title (題名) 探討半純函數指定兩個值之相關問題 zh_TW dc.title (題名) On meromorphic functions with two prescribed values en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] L. V. Ahlfors, Complex analysis, Third edition,McGraw-Hill, 1979. [2] J. B. Conway, Functions of one complex variable, Second edition, Springer-Verlag, 1973. [3] F. Gross, Factorization of meromorphic functions, U. S. Government Printing Office, Washington, D. C. , 1972. [4] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. [5] R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Gauthiers-Villars, Paris, 1929. [6] M. Ozawa, On the zero-one set of an entire function, Kodai Math. J. , 2 (1979), 194--199. [7] L. A. Rubel and C. C. Yang, Interpolation and unavoidable families of meromorphic functions, Mich. Math. J. , 20 (1973), 289--296. [8] L. Yang, Value distribution theory, Berlin Heidelberg: Springer-Verlag, Beijing:Science Press, 1993. [9] C. C. Yang and C. T. Chuang, Fixed points and factorization theory of meromorphic functions, Peking Univ. Press, 1988. [10] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, 2003. [11] H. X. Yi, Some theorems on systems of meromorphic functions, J. Shandong Univ. , 32 (1997), No.3, 241--247. zh_TW
